Due　to　the　demodulation　performance　of　traditional　envelope　demodulation　methods　depend　strongly　on　a　number　of　parameters　selected　by　experience　of　the　user,　so　an　adaptive　wavelet-based　envelope　method　derived　from　complex　shifted　Morlet　wavelet　is　proposed　to　overcome　this　shortcoming.　The　complex　shifted　Morlet　wavelet　family　is　adopted　to　extract　fault　features　based　on　the　fact　that　the　bearing　defect　can　excites　vibration　at　specific　impact　component.　Meanwhile,　based　on　the　optimal　principle　of　maximal　kurtosis　of　coefficient　waveform,　the　shape　parameters　of　Morlet　wavelet,　which　include　center　frequency　and　envelope　factor,　can　be　adjusted　adaptively　to　match　with　the　impact　component.　Thereby,　the　optimization　envelope　can　be　constructed　effectively.　Experimental　results　and　industrial　measurement　analysis　show　that　the　new　approach,　compared　with　the　common　complex　shifted　wavelet　transform,　could　effectively　extract　the　weak　fault　feature　with　the　optimal　matching　of　waveform,　and　is　suitable　to　extract　the　incipient　fault　feature　for　rolling　bearing.